A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newtons law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e., the temperature of its surroundings).

The equation for Newton's Law of Cooling is:

dT/dt = -k(T - Ts)

where:

• dT/dt is the rate of change of temperature,
• T is the temperature of the object,
• Ts is the temperature of the surroundings, and
• k is the cooling constant.

Given that the body cools from 3T to 2T in 10 minutes, we can set up the following equation:

∫(from 3T to 2T) dT/(T - T) = -k ∫(from 0 to 10) dt

Solving this equation gives us the value of k.

Next, we use this value of k to find the temperature of the body at the end of the next 10 minutes. We set up the following equation:

∫(from 2T to T') dT/(T - T) = -k ∫(from 10 to 20) dt

Solving this equation gives us the value of T', which is the temperature of the body at the end of the next 10 minutes.